# √Combine Like Terms?

• Dec 7th 2012, 07:42 PM
Enthusiast
√Combine Like Terms?
This is my first post, thank you for your consideration.

If it follows that
√8 = √2+4 = 2√2.

When why doesn't 2√2 + 2√2 = 2+2+√2+√2; instead of the correct answer of 4√2. How come the other like terms are discarted?

I know there is a super simple answer to this which will make me look like a complete mule, but I would rather be an informed mule than a proud fool.
• Dec 7th 2012, 09:14 PM
MarkFL
Re: √Combine Like Terms?
What you want is:

$\sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt{2}=2 \sqrt{2}$

and:

$2\sqrt{2}+2\sqrt{2}=2\sqrt{2}(1+1)=2(2\sqrt{2})=4 \sqrt{2}$
• Dec 8th 2012, 05:27 AM
Soroban
Re: √Combine Like Terms?
Hello, Enthusiast!

Welcome aboard!

Quote:

Why doesn't 2√2 + 2√2 = 2 + 2 + √2 + √2 ?

It should be obvious that we don't add like that.

$2\sqrt{2}$ is simply "two times a thing".

Let $x$ = thing.

Then you have: . $2x + 2x$

Got it?
• Dec 8th 2012, 04:36 PM
Enthusiast
Re: √Combine Like Terms?
I think I got really focused upon the deconstruction of the radicand and some how my "brain head" as Trippy would say got addition and multipication mixed up..(Itwasntme)..I don't know. Thanks for the clarification everyone.